Robust Output Regulation of Linear Passive Systems with Multivalued Upper Semicontinuous Controls

TL;DR

This paper develops a passivity-based control method using multivalued maximal monotone operators to robustly regulate the output of passive linear systems despite uncertainties and disturbances.

Contribution

It introduces a novel multivalued control law derived from maximal monotone operators, enhancing robustness in output regulation of passive linear systems.

Findings

Ensures output regulation despite parametric uncertainties and disturbances.

Demonstrates robustness properties through passivity analysis.

Provides numerical examples validating the control approach.

Abstract

The use of multivalued controls derived from a special maximal monotone operator are studied in this note. Starting with a strictly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how the multivalued control affects the dissipation equation of the closed-loop system, from which we derive its robustness properties. Finally, some numerical examples together with implementation issues are presented to support the main result.